Download Measures of Position

Measures of Position
Types of Measurements
(Standard Score)
• Standard Score: This score represents the number
of standard deviations a data value falls above or
below the mean. Symbol for standard score is z.
• Positive z score is above the mean, negative is
below the mean, and 0 is same score as the mean.
• Obtained by taking a data value – mean then
dividing by the standard deviation.
Standard Score Example 1
• Test A: Score was 72. Mean was 68. Standard
deviation was 5.
• Test B: Score was 81. Mean was 80. Standard
deviation was 2.
• On which test is the relative position better?
Types of Measurements (Percentiles)
• Percentiles: Position measures normally used in
the educational and health-related fields to
indicate position of an individual in a group.
• Percentiles are not the same as percentages.
Example: If students gets an 88% on a test that
does not indicate their position with respect to the
rest of the class. If 88% corresponds to the 80th
percentile than they did better than 80% of the
students in the class.
• Symbolized by P₁…P99 and divides the
distribution up into 100 parts.
Percentile Formula
• The percentile corresponding to a given value
(X) is computed by using the following
formula:
• Percentile = Number of values below +0.5 ● 100%
Total number of values
Percentile Examples
• A teacher gives a 30 point test to 12 students.
The scores are shown below. Find the
percentile rank of a score of 21.
(16,28,30,19,21,23,22,17,15,26,17,24)
• Step 1: Arrange data in order from least to
greatest.
• Step 2: Next substitute in the formula.
Finding values for a
corresponding percentile.
• Use the following set to find the value
corresponding to the 40th percentile.
(10,12,8,16,7,11,5,15,9,14)
• Step 1: Lowest to greatest
• Step 2: Compute using c = ( n ● p ) ÷ 100
• n = total number of values, p = percentile
• Step 3: If c is not a whole number round to next
whole number. If c is whole need to use average
of c and c +1 value.
Creating a percentile graph
• Use the data to create a percentile graph.
Class limit
19 - 25
26 - 32
33 - 39
40 - 46
47 - 53
Frequency
9
10
4
8
9
• Step 1: Create a cumulative freq. column and a
cumulative percent column.
• Step 2: Class boundaries create x-axis and
percents create y-axis.
Deciles, Quartiles, and Outliers
• Deciles: divide the data into 10 groups.
• Denoted by the symbol D1, D2,…D9 which
correspond to P10, P20,…P90.
• Quartiles: Divide the data into 4 groups.
• Denoted by the symbol Q1, Q2, Q3 which correspond to P25,
P50, P75.
• Outliers: Is an extremely high or low value when
compared to the rest of the data values.